Question: Simplify the following expression: $a = \dfrac{3}{10p} - \dfrac{4}{5p}$
In order to subtract expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $10p$ and $5p$ $\lcm(10p, 5p) = 10p$ $ a = \dfrac{1}{1} \cdot \dfrac{3}{10p} - \dfrac{2}{2} \cdot \dfrac{4}{5p} $ $a = \dfrac{3}{10p} - \dfrac{8}{10p}$ $a = \dfrac{3 -8}{10p}$ $a = \dfrac{-5}{10p}$ Simplify the expression by dividing the numerator and denominator by 5: $a = \dfrac{-1}{2p}$